Click on to the B92 wesbite (leading independent news outlet in Belgrade). It shows a page in Serbian but using the Latin script.

My Google Translator button helpfully asks if you would like it translated – "Always translate Croatian".

It does offer an option to translate this ‘Croatian’ into Serbian, which produces the same text but in Cyrillic.

Does Google not distinguish between Serbian and Croatian in themselves, simply calling Serbian written in the Latin script ‘Croatian’, and Croatian written in Cyrillic script ‘Serbian’?

Seems not. Go to Google Translator itself and it does recognise key language differences such as kruh (bread in Croatian) and hleb (in Serbian) but which it delivers in Cyrillic: